Intl. J. of Robotics Res. volume 21 number 10-11 Oct/Nov 2002

AbstractRobots to date lack the robustness and performance of eventhe simplest animals when operating in unstructuredenvironments. This observation has prompted an interest inbiomimetic robots that take design inspiration from biology.However, even biomimetic designs are compromised by thecomplexity and fragility that result from using traditionalengineering materials and manufacturing methods. Weargue that biomimetic design must be combined withstructures that mimic the way biological structures arecomposed, with embedded actuators and sensors andspatially-varied materials. This proposition is made possibleby a layered-manufacturing technology called ShapeDeposition Manufacturing (SDM). We present a family ofhexapedal robots whose functional biomimetic design ismade possible by SDM’s unique capabilities and whose fast(over 4 body-lengths per second) and robust (traversal overhip-height obstacles) performance begins to compare to thatseen in nature. We describe the robots’ design andfabrication and present the results of experiments that focuson their performance and locomotion dynamics.

KEYWORDS: Biomimetic Robots, Locomotion, ShapeDeposition Manufacturing

1. Introduction

Bending without Breaking

Unlike animals, robots to date lack the robustness andversatility needed to operate in unstructured environments.This observation has prompted interest in biomimetic robotsthat take design inspiration from biology. Examples includerunning [Raibert, 1986], swimming [Anderson et al., 1998]and flying [Yan, et al. 2001] robot prototypes.

Although biomimesis can take many forms, we believethe first step in making these efforts successful is to distillthe fundamental principles of effective animal performanceand then apply them to the robots’ design. It is impractical toattempt a direct mapping between morphologies, actuatorsor control schemes since biological systems face manyrequirements such as reproduction and respiration which arenot germane to the robot’s design.

However, even biomimetic designs are compromised bythe complexity and fragility imposed by traditionalfabrication methods. These methods rely on assemblies ofstiff metal structures, bearings and fasteners. The resultingdevices are both fragile and difficult to build, especially atsmall scales. Fasteners and connectors work loose, limbsbreak, and motors and bearings fail as they becomecontaminated with grit. (Fundamentally, a machine designedto be assembled can also disassemble itself.)

In contrast, nature’s mechanisms are robust. Sensors,actuators and structural materials are compactly integratedand enclosed, thereby protecting them against harsh externalconditions while avoiding stress concentrations that causefailure. Moreover, nature uses soft materials frequently andstiff materials sparingly [Vogel, 1995]. Even nominally stiffstructures such as cuticles, shells or bones, are rarely ofuniform stiffness and are connected or surrounded by softertissue. Part of the reason for the difference between humanand natural approaches may be a difference in philosophy.Nature’s guiding rule appears to be sufficient strength toavoid failure, not deformation.

Compliant materials in animals do more than providesturdiness in uncertain environments. They improveperformance and simplify control by providing mechanismsfor energy storage and return and for passive stabilization

Fast and Robust: Hexapedal Robots via Shape Deposition Manufacturing

Jorge G. ChamSean A. BaileyJonathan E. ClarkCenter for Design ResearchStanford UniversityStanford, CA 94305-2232, USA

Robert J. FullDept. Integrative BiologyUniversity of California at BerkeleyBerkeley CA 94720 USA

Mark R. CutkoskyCenter for Design ResearchStanford UniversityStanford, CA 94305-2232, USA

2

and disturbance rejection [van Soest and Bobbert, 1993;Brown and Loeb, 1997].

The advantages of compliance are also well established inrobotics. Most commonly, some form of impedance control[Hogan, 1985] is applied to a robot with stiff limbs. In thiscase, unexpected link collisions will still produce hightransient forces. Robots with compliant links have also beendeveloped but even in these robots, most of the damping isachieved via control. In our experience, passive dampers areoften considered at some point in designing a new robot orend-effector but ultimately abandoned due to the added cost,weight and complexity.

Our proposition is to make robots more like nature buildsits mechanisms, with biomimetic structures that integratecompliance and functional components such as sensors andactuators [Bailey, et al., 1999]. This proposition is madepossible by a layered-manufacturing technology calledShape Deposition Manufacturing (SDM) [Merz et al.,1994]. As described in detail later in the paper, SDM allowsus to “grow” robust mechanisms through a repeated cycle ofmaterial deposition and shaping. The mechanisms can havealmost arbitrary geometry with embedded actuators andsensors and heterogeneous structures with locally-varyingcompliance and damping. Although we can only begin toapproximate the elegance of biological structures, theresulting robots are simpler to control and more tolerant ofdamaging loads than comparable assembled robots.

Fast and Robust Legged Robots

The limitations in performance imposed by traditionalfabrication methods are particularly evident in legged robots

Figure 1. “Sprawlita,” a dynamically-stable runninghexapod based on functional principles derived frombiomechanical studies of the cockroach. The originalprototype is capable of running at 3.5 body-lengths persecond.

Legs with CompliantFlexures

Actuators andwiring embeddedinside structure

2.5 cm

for rapid traversal of rough terrain. Studies of thebiomechanics of running have shown that passive visco-elastic properties are at the heart of robust running[McMahon, 1984]. As described later in the paper, the basicmechanism for running in a variety of animals can bedescribed by a Spring-Loaded Inverted Pendulum (SLIP)[Cavagna, et al., 1975]. Raibert’s pioneering work [Raibert,1986] and contemporaries of our robots, such as RHex[Buehler, et al., 2000], are showing what is possible withsimple mechanisms.

In the following sections, we present a family of smallhexapedal robots whose fast (over 4 body-lengths persecond) and robust (traversal over hip-height obstacles)performance exceeds that of most current legged robots andbegins to compare with the performance seen in nature (seeFigure 1 and multimedia Extensions 1, 2 and 3). We firstdescribe their biomimetic design and fabrication and thenpresent results of experiments that focus on theirperformance and locomotion dynamics. Finally, we discussour conclusions and future work.

2. Functional Biomimetic DesignMuch recent interest in the field of walking and running

robots has been placed on the adoption of principles foundin animal locomotion [Ritzman et al., 2000]. The mostcommon instance of this biomimicry is seen in the largenumber of walking robots that utilize six legs in a variety ofgaits intended to maintain static stability [Bares et al., 1999;Waldron, 1986]. More recently, Case Western ReserveUniversity has experimented with duplicating the complexcockroach morphology [Nelson et al., 1997]. Dynamiclocomotion in animals has also received significantattention. For example, Raibert’s [1986] bouncing robotsdemonstrated the possibility of simple, dynamic runningmachines.

For the task of quick and robust traversal over uncertainterrain, we draw design inspiration from small arthropods.In particular, cockroaches are capable of remarkable speedand stability. For example, the American cockroach,Periplaneta americana, can achieve speeds of up to 50body-lengths per second [Full and Tu, 1991]. The Death’shead cockroach, Blaberus discoidalis, is capable oftraversing uneven terrain with obstacles up to three times theheight of its center of mass without appreciably slowingdown [Full et al., 1998]. Studies of these cockroachessuggest design principles for fast, stable, running hexapods:

1. self-stabilizing posture

2. thrusting and stabilizing leg function

3. passive visco-elastic structural elements

4. timed, open-loop/feedforward control

3

5. integrated construction.

The following sections describe these principles and howthey are implemented in the design and fabrication of ourprototypes (see Extension 4 for a demonstration of thesedesign principles).

2.1. Self-Stabilizing Posture

A sprawled hexapedal posture has several advantages.When walking, the center of mass can be maintained withina support polygon formed by at least three feet to ensurestatic stability. This approach, however, limits six-leggedrobots to walking slowly.

Observations of cockroaches running at high speeds, onthe other hand, show that their centers of mass approach andeven exceed the bounds of the triangle of support within astride [Ting et al., 1994]. Cockroaches achieve a form ofdynamic stability in rapid locomotion while maintaining awide base of support on the ground.

Kubow and Full [1999] suggest a further advantage to anappropriately sprawled posture with large forces along thehorizontal plane. Horizontal perturbations to a steadyrunning cycle are rejected by the resulting changes in thebody’s position relative to the location of the feet.Generalizing these results to a horizontal plane spring-massmodel revealed remarkable self-stabilizing properties(Schmitt, J. and Holmes, P., 2000a and 2000b).

Our first-generation prototype robot, approximately 16cmin length, was built for the simple task of fast straight-aheadrunning through rough terrain. Thus, it was designed with asimilar, but not identical, sprawled morphology only in the

Figure 2. Self-stabilizing posture: a rear and low centerof mass and a wide base of support contribute to the over-all stability of locomotion.

Center ofMass

ForwardDirection

ForwardDirection

5.5 cm

Top view

Side view

sagittal plane. The sprawl, or inclination, angle for each legis limited by foot traction; for larger animals (or robots), itbecomes progressively harder to sustain the necessarytangential forces. As shown in Figure 2, the center of masswas placed behind and slightly below the location of thehips, but still within the wide base of support provided bythe sprawled posture.

2.2 Thrusting and Stabilizing Leg Function

Using the stability provided by a tripod of support formedby at least three legs, many robotic walkers actuate the legsto move the robot’s center of mass forward whileminimizing internal forces in order to increase efficiencies[Kumar and Waldron 1990]. A common leg design places avertically-oriented joint at the hip to avoid costly torques forgravity compensation. The resulting “rowing” actionminimizes internal forces, but contradicts what is observedin the cockroach and other running animals.

Studies of the cockroach’s ground-reaction forces duringrunning indicate that legs act mainly as thrusters. Theground reaction forces for each leg point roughly in thedirection of the leg’s hip [Full et al., 1991]. In thecockroach’s sprawled posture, the front legs apply thisthrusting mainly for deceleration, while the hind legs act aspowerful accelerators. Middle legs both accelerate and

Figure 3. Studies of the cockroach’s locomotion showthat ground reaction forces are directed towards the hipjoints, indicating that the legs essentially act as thrusters.In addition, each leg performs a different function: frontlegs act as decelerators while hind legs act as accelerators;middle legs act as both.

CompliantSagittalRotary Joint

ActiveThrusting

Force

4

decelerate during the stride. The creation of large internalforces may be inefficient for smooth, steady-state running,but there is evidence it contributes to disturbance rejectionin heading and speed [Kubow and Full, 1999] and permitsrapid turning [Jindrich and Full, 1999].

A similar leg function has been designed in our robot asshown in Figure 3. The primary thrusting action isperformed by a prismatic actuator, here implemented as apneumatic piston. The piston is attached to the body througha compliant rotary joint at the hip. This unactuated rotaryjoint is based on studies of the cockroach’s complianttrochanter-femur joint, which is believed to be largelypassive in the sagittal plane. In the prototype, the complianthip joint is constructed as a flexure of visco-elastic materialthat allows rotation mainly in the sagittal plane, as shown inFigure 3.

These active-prismatic, passive-rotary legs are sprawledin the sagittal plane to provide specialized leg functionsimilar to that in the cockroach. Servo motors orient the hipswith respect to the body, thus setting the nominal, orequilibrium, angle about which the leg will rotate. Bychanging this angle, we can affect the function that the legperforms by aiming the thrusting action towards the back (toaccelerate) or towards the front (to decelerate).

2.3 Passive Visco-elastic Structure

As mentioned, animals are commonly anything but rigid.In particular, studies of the cockroach Blaberus discoidalisare revealing the role of the viscoelastic properties of itslimbs in locomotion [Garcia et al., 2000; Meijer and Full,2000; Meijer and Full, 1999]. This visco-elasticity resides

Figure 4. Suggested roles of a feedforward motor pattern,preflexes and sensory feedback. Here, disturbancerejection is the result of the mechanical system and not anactive neural control loop. Adapted from [Full andKoditschek, 1999].

MechanicalSystem

(muscles, limbs)

Environment

MechanicalFeedback(Preflexes)

SensoryFeedback(Reflexes)

Neural System(CPG)

FeedforwardMotor Pattern

Passive DynamicSelf-Stabilization

Locomotion

not only in the limbs’ joints, but also in their muscles andexoskeleton.

Our prototype’s legs contain a passive rotary hip jointfabricated as a flexure of viscoelastic urethane embedded ina leg structure of stiffer plastic. The flexures, like thecockroach’s limbs, dissipate significant energy throughhysteresis, as evidenced by force-displacement plots of thematerial under sinusoidal loading [Xu et al., 2000]. The legsexhibit slightly underdamped behavior when not in contactwith the ground. These leg flexures are an initial attempt atintegrating desired impedance properties into the structureof the robot itself. Although it primarily allows rotation inthe sagittal plane, the joint provides some compliance in theother directions as well.

2.4 Open-Loop/Feedforward Control

The self-stabilizing properties of the visco-elasticmechanical system and functional morphology mentionedabove have been termed “preflexes” [Brown and Loeb,1999]. These preflexes provide an immediate, or “zero-order” response to perturbations without the delays of neuralreflexes. Studies of the cockroach running over uneventerrain suggest that these preflexes play a dominant role inthe task of locomotion. For example, there are only minorchanges in the cockroach’s muscle activation pattern as itrapidly transitions from smooth to uneven terrain [Full et al.,1998]. There is no carefully controlled foot placement ornoticeable changes in gait pattern. These findings suggest acontrol hierarchy, as shown in Figure 4 [Full andKoditschek, 1999].

In this scheme, the basic task of locomotion isaccomplished by a properly tuned mechanical systemactivated by a feedforward, or open-loop, control input. Thiscombination effectively provides a mechanical “closed-loop” that is sufficient to maintain stability in the face ofperturbations or terrain changes [Cham et al., 2000;Ringrose, 1997]. Sensory information is then used to modify

Figure 5. A comparison of isometric muscle force output[Full and Meijer, 2000] in response to motor commandsand pneumatic piston force output in response to solenoidvalve input on Sprawlita.

Fo

rce

(N)

5

20 40 60 80

Pre

ssu

re (

psi

)

80

1000Time (ms)

Valve ON

FootContact

0 20 40 60 80 1000

0.6

Fo

rce

(N)

Time (ms)

MuscleCommands

Valve OFF

5

the feedforward pattern to change the animal’s behavior inorder to adapt to changing conditions. For example, rapidturning may be effected simply by changing the amount offorce production in the legs [Jindrich and Full, 1999].

Our robot is controlled by alternately activating tripods,composed of a front and rear leg on the same side and amiddle leg on the opposing side. Each of these tripods ispressurized by a separate 3-way solenoid valve, whichconnects the pistons to either a pressurized reservoir or theatmosphere. The valves are operated at a frequency andduration determined respectively by the stride period andduty cycle of a binary on/off activation pattern. For initalexperiments this simple stride pattern was provided througha tether by an off-board computer. In subsequentexperiments, a small, on-board computer provides thispattern. Current work focuses on adaptation, or self-tuning,of this pattern to changing terrain conditions using onlybinary ground-contact information from the robot’s feet[Cham et al., 2001].

Despite the binary activation of the valves, the forceoutput is surprisingly muscle-like in profile as shown inFigure 5. The compressibility of air, the tubing lengths,valve porting, and small piston orifices conspire totransform the square wave valve input into a gradual build-up of force and stiffness that reduces the impact when feetstrike the ground.

The feedforward controller also commands the nominalangle for each hip, which determines foot placement andthrust direction. However, these angles are not changedwithin each stride, but are instead servoed in response tochanges in the desired task. For example, forward andbackward velocity as well as turning radius are a function ofthe nominal angles of each hip. In a later section, we will see

Figure 6. ShapeDeposition Manufact-uring (SDM) consists ofalternating cycles ofmaterial deposition andshaping. The hexapod’sservos and wiring wereembedded inside thestructure of the body.As shown in the figure,they were first placed ina shaped geometry ofsupport material andthen encased bydepositing material inthe following step.

Shape Support Material

Embed servos & wiring

Deposit and Shape Body MaterialDeposit

Shape

Embed

Finished Part

the performance of this simple control scheme, and theeffects of changing the feedforward pattern.

3. Fabrication of Biomimetic StructuresThe preflexes, or passive mechanical properties,

mentioned above, could theoretically be constructed orapproximated using traditional manufacturing methods. Atsmall scales, however, this becomes impractical for severalreasons. First, design and assembly become difficult as thestructure’s volume is increasingly dominated by fastenersand connectors at small scales. Second, these connectorsoften fail under the collisions and falls that are unavoidablein running over rough terrain. Finally, assembled off-the-shelf compliant elements are nearly impossible to “tune,”that is, to create with desired spatial compliance anddamping properties. This section describes a manufacturingprocess that circumvents these problems and makespractical the application of nature’s design lessons in ourprototype robots.

Shape Deposition Manufacturing (SDM) is a layeredprototyping method in which parts or assemblies are built upthrough a cycle of alternating layers of structural andsupport material. Unlike other rapid-prototyping processes,SDM shapes each layer of material on a computer-controlled milling machine after it is deposited. This allowsfor high precision features and avoids the common stair-stepping effect. The intermittent addition of sacrificialsupport material allows for the construction of nearlyarbitrary geometries and facilitates the inclusion ofembedded components (see Extension 5). The process isdescribed in greater detail in [Merz et al., 1994; Binnard andCutkosky, 2000].

6

Figure 6 shows the basic cycle of the process, illustratedby in-process pictures of the fabrication of the robot’s body.SDM’s capability of embedding components inside the partin a precise and repeatable fashion [Cham et al., 1999] wasused to create the robot’s body with embedded servos andwiring. This was done by first shaping the support substrate(high melting-temperature wax) as a mold for the bottom ofthe body. The embedded components were then placed, withtheir moving parts encased in sacrificial material (lowmelting-temperature wax), to prevent later intrusion ofplastic. A layer of structural material (pourablepolyurethane) was then deposited and shaped, therebyencasing the embedded components. Finally, the sacrificialmaterial was removed from the finished part to access theservos.

The construction of the multi-material compliant legs, asshown in Figure 7, takes advantage of SDM’s capability tovary the material properties during construction (seeExtension 6). Each layer was built up of a different material,each with its own characteristics. The deposition of a layerof soft viscoelastic polyurethane creates the compliant,damped hip flexure. A stiffer grade of polyurethane wasused for the structural members, which encase the pistonand servo mounting. These leg structures have proven to berobust and have undergone over a million cycles withoutfailure.

Modeling has been done to compare the properties ofthese polyurethanes with the material characteristics found

Figure 7. Process plan for the robot legs. The figure showsthe alternating layers of hard and soft material andembedded components used to make the compliant legs.

Structural Material

Sacrificial Wax

Embedded Piston

Support Wax

Compliant Material

Structural Material

Embedded Fitting

Support Wax

Embed/Deposit

Shape

Deposit

in the exoskeleton of cockroaches. It was found that, fornormal running frequencies, a simple viscoelastic materialmodel can be fit to both the biological materials and thepolyurethanes [Xu et al., 2000].

4. Results: Performance Testing.

This section presents results of velocity tests anddiscusses initial attempts to understand the role of therobot’s “preflexes” on this performance metric. The resultspresented here are for our first-generation prototype,“Sprawlita,” whose maximum speed is 55 cm/s, or 3.5 body-lengths per second. More recent prototypes, not reportedhere, are designed to minimize pneumatic delays by usingone solenoid valve per leg. These prototypes can run at 70cm/s, or approximately 4.5 body-lengths/s (see Extension 3and 7).

The basic mechanism for locomotion in the robot isshown in Figure 8 (see also Extension 8). As shown, therotational compliance in the legs is essential in generatingmotion. At the beginning of the half-stride (a), the tripod hasjust made contact with the ground and the hip deflectionsare small. Near the end of the half-stride (b), the pistons areat full stroke and the compliant hips are significantlydeflected. Once the tripod is retracted, the legs passivelyreturn to their equilibrium positions.

Variations in stride period, tripod duty cycle and nominalleg angles have a significant effect on the speed oflocomotion. Moreover, the optimal parameter settings varyas a function of the slope and hardness of the terrain. Forexample, Figure 9 shows how the velocity varies as afunction of the slope for two different stride periods. Asseen, the shorter period results in faster performance onlevel ground. But for slopes of greater than 12 degrees thelonger period is preferable.

To better understand the most important factorsinfluencing the speed of locomotion we performed a partialfactorial set of experiments [Box and Bisgaard, 1988] for

Figure 8. High-speed footage of the running robot in a)mid-stance and b) full extension. As shown, thecompliance in the legs plays an important role in thelocomotion, as evidenced by the large deflections duringthe stride.

(a) (b)

7

the following parameters: stride period, duty cycle, front hipangle, middle hip angle, rear hip angle, and flexurecompliance.

The parameter variation experiments were conducted onlevel ground and at a moderate slope of 8 degrees. High andlow values were chosen empirically based on reasonablevalues for level ground and hill climbing. Under theexperiment’s conditions, the maximum speed on smoothlevel ground was 42cm/s or approximately 2.5 body lengthsper second. The most significant factors affecting the speedof locomotion were, in decreasing order of significance: hipcompliance, rear leg angles, front leg angles, and strideperiod. These results emphasize the importance of properlytuning the impedance properties of the system. For runninguphill the most significant parameters to vary, again indecreasing order of significance, were stride period, rear legangles, and front leg angles. This agrees with the testsshown in Figure 9 and suggests the importance of adaptationof the basic feed-forward pattern to match changes in theenvironment.

On flat, even terrain, the robot is able to clear obstacles3.5cm high corresponding to its ground clearance, or one“belly-height” (see Extension 9). As slope increases, theheight of the maximum obstacles decreases. The ability tomove across various ground conditions was also tested.

24 deg.

(a) (b)

(c)

Velocity vs. Slope for Different Gait Periods

0

20

40

60

-12 -4 4 12 20Slope (deg)

Vel

ocity

(cm

/s)

Gait Period = 210 ms (5 Hz)

Gait Period = 90 ms (11 Hz)

Figure 9. Performance test results. The prototype iscapable of surmounting a) uphill slopes of up to 24degrees and b) hip-height obstacles. c) Tests over differentslopes indicate the need to adapt the variables oflocomotion to environmental conditions.

While the robot is capable of moving across different soilssuch as sand, foot design is important to prevent miring (seeExtension 10).

5. Results: Locomotion DynamicsAs our prototype “Sprawlita” scurries across the floor and

over obstacles, the combination of the “preflexes” and open-loop control scheme result in insect-like locomotion.However, a closer examination of the ground reaction forcesand center-of-mass trajectories reveals some differences tothe cockroach’s locomotion. This section detailsexperiments to compare the locomotion dynamics ofSprawlita to that of its exemplar, Blaberus discoidalis, interms of two metrics commonly used in biomechanicalstudies: pendulum-like energy recovery and ground-reactionforce patterns.

5.1 Basis for Comparison: Walking and Running Models of Animals

In animals there are very distinct patterns of force andmotion when walking or running [Cavagna, 1975; Blickhanand Full, 1987]. During walking, the kinetic and potentialenergies of the center of mass fluctuate out of phase in asinusoidal manner. Theoretically, the potential and kineticenergies can be exchanged via a pendulum-like energyrecovery mechanism.

In contrast, running in animals is characterized by thekinetic energy and potential energy fluctuating in-phase,eliminating the possibility of pendulum-like energyexchanges. This type of motion can be characterized bywhat is called the spring loaded inverted pendulum (SLIP)model. This model also produces a characteristic set ofground reaction patterns, with the vertical force leading thehorizontal force by a phase difference of 90 degrees[Cavagna, 1975].

Figure 10. Apparatus for experiments: High-speed videoand markers were used to track the robot’s trajectory; aforce plate measured ground reaction forces for both thewhole body and for individual feet.

Force Plate

Sagittal PlaneTrajectory ofCenter of Mass

Ground ReactionForce Vectors(minus gravity)

RunningDirection

High-speed Footage

8

SprawlitaBlaberus discoidalis

Vertical

Horizontal

Vertical

Horizontal

Force (N)

Velocity (m/s)

Displacement (m)

Kinetic Energy (J)

Potential Energy (J)

Total Energy (J)

Vertical

Vertical

Vertical

Horizontal

x10-3

x10-4

x10-7

x10-5

x10-6

x10-5

x10-4

Tripod 1

Tripod 2

Active Legs

Half-stride Stride period

AB

C

D

EF

G

H

I

J

K

L

M

N

O

PQ

0 40 80 0 60 120Time (ms) Time (ms)

Figure 11. The results of force plate and high-speed video experiments described in Section 3 show certain differencesin the locomotion of Blaberus discoidalis [Full and Tu, 1990] and Sprawlita. The respective amounts of pendulum-likeenergy recovery, calculated from the center-of-mass energetics, indicate that neither hexapod is “walking.” Therespective ground reaction force plots show that the standard model of animal running, the spring-loaded invertedpendulum (SLIP) model, fits the cockroach and the robot well, with some differences due to foot dragging. Labels (A) -(Q) correspond to features discussed in Sections 5 and 6.

9

Ground reaction force patterns and pendulum-like energyrecovery measures help qualitatively determine how mucheach basic mechanism of locomotion is utilized.

5.2 Equipment and Methods: Cockroach Measurements

Position, velocity and ground reaction forcemeasurements for the Blaberus discoidalis cockroach (meanmass 0.0026kg) were obtained in [Full and Tu, 1991]. Insummary, the cockroaches were run along a track with aforce platform while a high-speed video system captured thelocomotion at 60 frames/second. Kinetic and potentialenergy data were calculated by integrating the force signals.Stride beginnings and endings were determined by verticalground reaction force patterns and verified using videoinformation.

5.3 Equipment and Methods: Robot measurements

Sprawlita (mass 0.275kg) was run along a plywoodsurface, with reflective markers attached to nose, back, eachleg, and each foot. A high-speed video system captured thelocomotion at 250 frames per second. The force platformwas a modified 6-axis force-sensitive robotic wrist. Analuminum plate covered with a thin rubber layer to preventslippage, as shown in Figure 10, was attached to the forcewrist and placed flush with the plywood surface. The naturalfrequency of the force plate was 143Hz. Forces were filteredby an analog 4th order Butterworth filter at 100Hz, and thensampled at 1000Hz and converted to a digital signal. Forceswere then digitally filtered at 50Hz by a Butterworth filterwith zero phase shift. The minimum resolution of the forceplate is approximately 0.1N in the vertical and fore-aftdirections.

Center of mass position data were calculated by trackingthe reflective markers attached to the body. Velocity wascalculated by taking the derivative of the position data. As

Figure 12. Ground reaction force vectors superimposed onto position data for an entire stride period. The vertical axisof the middle plot is exaggerated for detail. The ground reaction force vectors shown have been compensated forgravity by subtracting the weight of the robot from the vertical force measurement.

ExaggeratedCOM Sagittal

Trajectory

Ground reactionforce vectorscompensated

for gravity

COM SagittalTrajectory

SprawlitaBlaberus discoidalis

with the cockroach, stride beginnings and endings weredetermined by vertical ground reaction force patterns, andverified using video information.

5.4 Biomimetic Comparison: Pendulum-like Energy Recovery

As discussed previously, a significant amount of energymay be available for recovery during walking via apendulum-like energy recovery mechanism. In animals, thismechanism is used extensively, as energy recovery valuesapproach 70% in walking humans [Cavagna, 1975] and 50%in crabs [Blickhan and Full, 1987]. This measure can becalculated by:

Here, ΣHKE is the sum of the positive changes inhorizontal kinetic energy during one stride, ΣGPE is the sumof the positive changes in gravitational potential energyduring one stride, and ΣTE is the sum of the positivechanges in the total mechanical energy of the center of massduring one stride. If there is only one peak in the givenenergy measure per stride, then the sum of the positivechanges is simply the amplitude. In addition, vertical kineticenergy is typically excluded from these calculations as it isgenerally negligible in comparison to the other energies.Typical pendulum-like energy recovery is about 2% inrunning animals [Cavagna, 1975]. Thus, this metric is aquantitative indication of whether the observed locomotionis well represented by an inverted pendulum model,indicating walking dynamics.

The pendulum-like energy recovery values for a runningcockroach are quite low, with a mean of 15.7%. This is aresult of the kinetic energy leading the potential energy byonly 7.6 degrees as shown in Figure 11 (P). While this is not

ΣHKE ΣGPE+( ) ΣTE–ΣHKE ΣGPE+

-------------------------------------------------------------x100%

10

surprising for the animal during fast locomotion, it isinteresting that even at one-quarter the maximum stridefrequency (3Hz), the amount of pendulum-like energyrecovery is low. At very low speeds, locomotion becomesintermittent, taking only a few quick strides at a time. Thusit seems that this animal actually prefers a running gait.

As shown in Figure 11 (Q), the phase difference betweenthe kinetic and potential energies in our robot would seem toplace its locomotion closer to the inverted pendulum modelobserved in walking animals than to the running modelobserved in the cockroach. Here, the kinetic energy leads thepotential energy by approximately 60 degrees. However, theactual calculated value of pendulum-like energy recoveryfor Sprawlita is relatively low at 10.2%. This low value isdue to the non-sinusoidal shapes of the energetics and thelarge difference between the magnitudes. Thus, like thecockroach, the robot does not exhibit the pendulum-likeenergy recovery associated with walking. However, thereare still some dynamic differences which are evident in acomparison of ground reaction forces.

5.5 Biomimetic Comparison: Ground Reaction Forces

The ground reaction forces produced by Blaberusdiscoidalis are what one would expect for a running animalwith bouncing dynamics. During the first part of a half-stride, the fore-aft horizontal force applies a braking force,slowing the body down as shown in (A) of Figure 11. As thehalf-stride progresses, the fore-aft force changes directionand an accelerating force is produced (B), causing the bodyto increase speed, with maximum horizontal velocityattained at the end of half-stride (C). In short, there is a clearbrake-propel pattern over the course of each half-stride.

Figure 13. Plots of the individual leg ground reactionforces for Blaberus discoidalis [Full et al., 1991] andSprawlita. As indicated, dragging occurs in the middleand rear legs of Sprawlita during locomotion. This andthe relative lack of deceleration provided by the frontlegs account for differences in locomotion dynamics.

time time time

timetimetimeFront Middle Back

BackMiddleFront

Blaberusdiscoidalis

0 0 0

0 0 0

Sprawlita

Vertical

forc

e

forc

e

forc

e

forc

e

forc

e

forc

e

Horizontal

As shown in Figure 11, the vertical force pattern is just asdistinctive. The vertical force is a minimum at the beginningof a half-stride (D) and increases to a maximum that occursduring in the middle of the half-stride (E). The vertical forcethen returns to the minimum by the end of the half-stride(F), resulting in a maximum vertical displacement as thecockroach switches from one tripod of legs to another (G).In short, the vertical force oscillates about the weight of thebody in a minimum-maximum-minimum pattern over thecourse of the half-stride.

The aggregate of these fore-aft and vertical force patternsas shown in Figure 12 verify that the overall body motion ofthe cockroach is well characterized by the spring-loadedinverted pendulum model and is dynamically similar toother animals during running [Cavagna, 1975; Full andFarley, 2000].

As shown in Figure 11, the vertical force patternsgenerated by the robot are quite similar to the cockroach. Atthe beginning of the half-stride, the vertical force is aminimum (H), very close to zero. Midway through the half-stride, the vertical force peaks (I) and then decreases backtowards the minimum by the end of the half-stride (J),resulting in a maximum displacement near the tripod switch(K). As with the cockroach, there is a clear minimum-maximum-minimum pattern over the half-stride.

The fore-aft horizontal forces, on the other hand, begin toshow some dissimilarities. As in the cockroach, the fore-aftforces begin the half-stride at a minimum (L), deceleratingthe body, and increase to a maximum (M), accelerating thebody. Considering only this portion of the half-stride, thereis a brake-propel cycle in both the animal and the robot.However, the latter part of the half-stride shows a pattern oflight vertical forces (J) and decelerating fore-aft forces (N),resulting in an early horizontal velocity peak (O). Thisdifference in the horizontal forces explains the large phasedifference between the kinetic and potential energies asdiscussed earlier.

Examination of the video data reveals that the robotassumes a “pseudo-flight” phase in which the middle andrear feet never quite leave the ground. Instead, they dragalong in light contact, which accounts for the differing forcepatterns. The phenomenon is a result of the thrusting pistonsreaching the end of their stroke before the stride is complete.At the same time, the torsional elements in the hips applytorques to the legs which keep the feet in contact with theground.

5.6 Biomimetic Comparison: Individual Leg Ground Reaction Forces

There are many ways in which the SLIP model groundreaction force patterns can be produced by a system withmultiple legs. In contrast to the Raibert approach of running

11

with symmetry [Raibert, 1986], each of the cockroach’s legscarries out very different functions in producing the SLIP-like behavior. While the vertical force patterns forindividual limbs are similar, forces in the fore-aft directionare quite different. In general, the front legs decelerate, therear legs accelerate, and the middle legs do both, as shownin Figure 13.

When we examine the plots in Figure 13, we see that thereare some differences between the individual leg functions inthe cockroach and the robot. While the rear legs accelerateduring the first part of the half-stride, there is a negativefore-aft force during the latter part of the half-stride due todragging. When we consider the middle leg force profile, wesee that it is almost the opposite of the cockroach's. Themiddle legs initially provide acceleration, and thendeceleration. As shown, the front legs do not provide muchdeceleration.

6. Results: DiscussionSprawlita has demonstrated the feasibility of small,

sturdy, biomimetic robots that exploit passive properties incombination with an open-loop controller to achieve fast,stable locomotion over obstacles. As shown, thisperformance is highly dependent on the robot’s compliantelements and mechanical configuration, and underscores the

Figure 14. Multi-material prototype leg extensionmechanism made from two materials: a rigid material forthe links and a soft material (reinforced with polyesterfibers) for the flexures. A comparable mechanismassembled from off-the-shelf components would be morecumbersome, fragile and difficult to fabricate (seeExtension 11).

Rigid Material

Soft Material

importance of SDM’s ability to tailor these passiveproperties.

While Sprawlita's scurrying is insect-like, a comparison ofthe ground reaction forces reveals some differences to itsexemplar, particularly in the horizontal direction. A closerinspection of the individual leg forces shows somedifferences to the cockroach in the behavior of the front,middle and rear legs. Instead of being decelerated primarilyby the front and middle legs at the end of each stride,Sprawlita is partly decelerated by foot dragging in the rearlegs. As a consequence, the robot does not display thetypical phasing of horizontal and vertical forces associatedwith the SLIP model found in running animals. In essence,the rear legs are “running out of stroke length,” resulting in apseudo-flight phase with dragging feet.

These observations suggest modifications forincorporation into the next generation of biomimetichexapods. In particular, we can increase the stroke length ofthe middle, and especially the rear legs by embeddingcustom pistons with a longer stroke length or by fabricatinga compliant SDM linkage that multiplies the pistons'motion, such as the one shown in Figure 14. We anticipatethat if we can prevent the pseudo-flight phase and footdragging, the front and middle legs will be able to take onthe role of compliantly decelerating the robot at the end ofeach stride, and a more elegant SLIP-like motion will beobserved. Whether this motion will truly be faster or morerobust remains to be verified, but given its ubiquity inrunning animals it is certainly worth investigating.

7. Conclusions and Future WorkAt the moment, state-of-the-art legged robots, including

ours, are not capable of much better performance than smallwheeled vehicles with suspensions and treaded tires.Nonetheless, the advantages of legged systems are wellestablished. Cockroaches are capable of faster speeds andtraversal over more rugged terrain than any wheeled systemof similar scale. The prototypes presented here begin toapproximate that performance, and are faster, more robustand simpler than most previous legged robots. The successof these running hexapedal robots is based on designprinciples taken from biological studies of function inrunning animals.

These principles were made realizable in a robust mannerthrough the use of Shape Deposition Manufacturing. Theuse of this technology allowed us to embed functionalcomponents and create visco-elastic flexures in structureswithout fasteners and connectors that are often the cause offailures due to stress concentrations. The use of traditionalassembly-based manufacturing methods would have limitedthe robot’s performance and robustness.

12

The application of SDM in these prototypes represents asimple demonstration of the capabilities of the process.SDM allows roboticists to embed actuators and sensors instructures of arbitrary geometry, while tailoring thestructures’ passive properties. Future work in the area ofSDM continues to explore the process’ capabilities and todevelop a design interface that allows roboticists that arenew to the process to quickly generate and modifymanufacturing plans [Clark et al, 2001]. Furthermore, weadvocate that the use of SDM is not limited to robots whosedesign is directly inspired by biology. Rather, SDM canprovide a solution in any robotic application whereintegration of the robot’s structure and active componentswould improve its performance and robustness, especially atsmall scales. The relative advantages of the process forlarger-scale mechanisms remain an open question.

Future work will also continue on the development ofrobust running robots. As shown, the simple open-loopcontrol scheme is sufficient for straight-ahead running oversmooth and uneven terrain. However, our results also showthe need for adaptation. Different environmental conditionssuch as slope and texture require different sets of operationalparameters for optimal traversal. Future work will focus onaugmenting the current control structure to allow adaptationto changes in environment and task.

AcknowledgementsThe authors thank the members of the Berkeley

PolyPEDAL lab and the Stanford CDR and RPL teams fortheir contributions to the work documented in this paper. Inparticular, we thank Kenneth Meijer, Mike Binnard, RogerGoldman and Motohide Hatanaka. Sean Bailey is supportedby an NDSEG fellowship. This work was supported by theNational Science Foundation under grant MIP9617994 andby the Office of Naval Research under N00014-98-1-0669.

ReferencesAnderson J M, Streitlien K, Barrett D S, Triantafyllou M S

“Oscillating foils of high propulsive efficiency.” JFluidMech.360:41-72, 1998

Bailey, S. A., Cham, J. G., Cutkosky, M. R., and Full, R. J.,“Biomimetic Mechanisms via Shape DepositionManufacturing,” in Robotics Research: the 9thInternational Symposium, J. Hollerbach and D.Koditschek (Eds), Springer-Verlag, London, 1999.

Bares, John E. and Wettergreen, D. S. "Dante II: technicaldescription, results, and lessons learned" InternationalJournal of Robotics Research v 18 n 7 p 621-649, 1999.

Binnard, M. and Cutkosky, M. R., “A Design byComposition Approach for Layered Manufacturing”ASME Transactions, J. Mech. Design, vol. 122, no. 1,March 2 p. 91-101, 2000.

Blickhan, R., and Full, R.J., “Locomotion energetics of theghost crab. II. Mechanics of the centre of masss duringrunning and walking,” J. exp. Biol., 130, 155-174, 1987.

Box, G. and Bisgaard, S., Statistical tools for improvingdesigns. Mechanical Engineering Magazine, 110(1):32-40, January 1988.

Brown, I.E. and Loeb, G.E., "A reductionist approach tocreating and using neuromusculoskeletal models." InBiomechanics and Neural Control of Posture andMovement. (Eds. Winters, J. M. and Crago. P. E.), 1999.

Buehler, M., Saranli, U., Papadopoulos, D., and Koditschek,D. E., "Dynamic locomotion with four and six-leggedrobots," International Symposium on Adaptive Motion ofAnimals and Machines, Montreal, Canada, August, 2000.

Cavagna, G. A., Heglund, N. C., and Taylor, C. R.,“Walking, Running, and Galloping: MechanicalSimilarities between Different Animals,” Scale Effects inAnimal Locomotion, Proceedings of an InternationalSymposium, T. J. Pedley (Ed.), 111-125, Academic Press,New York, USA, 1975.

Cham, J. G., Karpick, J., Clark, J. E., and Cutkosky, M. R.,"Stride Period Adaptation for a Biomimetic RunningHexapod,” 10th International Symposium of RoboticsResearch, Lorne, Victoria, Australia, November 9-12,2001

Cham, J. G., Bailey, S. A., and Cutkosky, M. R., “RobustDynamic Locomotion Through Feedforward-PreflexInteraction,” ASME IMECE Proceedings, Orlando,Florida, November 5-10, 2000

Cham, J. G., Pruitt, B. L., Cutkosky, M. R., Binnard, M.,Weiss, L. E., Neplotnik, G., "Layered Manufacturing withEmbedded Components: Process Planning Issues," ASMEProceedings, DETC '99, Las Vegas, Nevada, September12-15, 1999.

Clark, J., Xia, L. and Cutkosky, M. R., “An interactive aidfor designing and planning heterogeneous layeredprototypes,” To be published in ASME Proc., DETC 2001,Pittsburgh, PA, 2001.

Full, R. J. and Meijer, K., “Artificial muscles versus naturalactuators from frogs to flies,” In Smart Structures andMaterials 2000: Electroactive Polymer Actuators andDevices (EAPAD) (ed. Yoseph Bar-Cohen). Proc. SPIEVol. 3987, p. 2-9, 2000.

Full, R. J., and Tu, M. S., “Mechanics of a Rapid RunningInsect: Two-, Four-, and Six-legged Locomotion,” Journalof Experimental Biology, 156, 215-231, 1991.

Full, R. J., and Tu, M. S., “Mechanics of Six-leggedRunners,” J. Exp. Bio., 148, 129-146, 1990.

Full, R. J., Autumn, K., Chung, J. I., Ahn, A., “Rapidnegotiation of rough terrain by the death-head cockroach,”American Zoologist, 38:81A, 1998.

Full, R. J., Blickhan, R. and Ting, L. H., “Leg design inhexapedal runners” J. exp. Biol. 158, 369-390, 1991.

13

Full, R.J. and Farley, C. T., “Musculoskeletal dynamics inrhythmic systems - a comparative approach to leggedlocomotion,” in Biomechanics and Neural Control ofPosture and Movement, J. M. Winters and P. E. Crago(Eds.), Springer-Verlag, New York, 2000.

Full, R.J., Koditschek, D. E., "Templates and Anchors -Neuromechanical hypotheses of legged locomotion onland." In Designs for Life. The Journal of ExperimentalBiology. In press.

Garcia, M., Kuo, A., Peattie, A. M., Wang, P. C. and Full, R.J., “Damping and Size: Insights and BiologicalInspiration” in Proc. of the Intl. Symp. on AdaptiveMotion of Animals and Machines, Montreal, Canada,August 2000.

Hogan, N. Impedance Control: An Approach toManipulation: Part I-Theory. Journal of Dynamic Syst.,Measure, and Cont., 107(1):1-7, 1985a.

Jindrich, D.L. and Full, R.J. Many-legged maneuverability:dynamics of turning in hexapods. J. exp Bio. 202, 1603-1623, 1999.

Kubow, T.M., Full, R.J., "The role of the mechanical systemin control: A hypothesis of self-stabilization in hexapedalrunners." Phil. Trans. Roy. Soc. London B. 354, 849-862,1999.

Kumar, V. and Waldron, K., "Force Distribution in Walkingvehicles," ASME Transactions, Journal of MechanicalDesign, Vol. 112, pp. 90-99, March 1990.

McGeer, T., “Passive dynamic walking,” IJRR, Volume 9,62-82, April 1990.

McMahon, T. A., “Muscles, Reflexes and Locomotion”University Press, Princeton NJ.

Meijer, K. and Full R. J., “Stabilizing properties of the coxa-femur extensor muscles of the cockroach (BlaberusDiscoidalis). Society of Experimental Biology, Exeter,England, 2000.

Meijer, K., Full, R. J., “Stabilizing properties of invertebrateskeletal muscle,” American Zoologist, Volume 39,Number 5, 117A, 1999.

Merz, R., Prinz, F.B., Ramaswami, K., Terk, M., Weiss, L.,"Shape Deposition Manufacturing," Proceedings of theSolid Freeform Fabrication Symposium, University ofTexas at Austin, August 8-10, 1994.

Nelson, G. M., Quinn, R. D., Bachmann, R. J., Flannigan,W. C., Ritzmann, R. E., and Watson, J. T., “Design andSimulation of a Cockroach-like Hexapod Robot,”Proceedings of the 1997 IEEE International Conference onRobotics and Automation, Albuquerque, NM, 1106-1111,1997.

Raibert, M. H., "Legged robots that balance." MIT Press,Cambridge, MA, 1986.

Ringrose, R., "Self-stabilizing running," IEEE ICRAProceedings, Albuquerque, NM, 1997.

Ritzman, R. E., Quinn, R. D., Watson, J. T. and Zill, S. N.,

“Insect Walking and Biorobotics: A Relationship withMutual Benefits” January / Vol. 50 No. 1 o BioScience23-33, 2000.

Schmitt, J. and Holmes, P., “Mechanical models for insectlocomotion: dynamics and stability in the horizontal planeI, Theory,” Biol. Cybern. 83, 501-515, 2000a.

Schmitt, J. and Holmes, P., “Mechanical models for insectlocomotion: dynamics and stability in the horizontal planeII, Application,”. Biol. Cybern. 83, 517-527, 200b.

Ting, L.H., Blickhan, R. and Full, R.J. Dynamic and staticstability in hexapedal runners. J. exp Bio. 197, 251-269,1994.

van Soest, A. J., Bobbert, M. F., “The contribution ofmuscle properties in the control of explosive movements”in Biol. Cybernetics 69: 195-204, 1993

Vogel, S. “Better bent than broken” Discover, p62 - 65, May1995.

Waldron, KJ "Force motion management in leggedlocomotion." IEEE Trans on Robotics and Automation. 2(4): 214-220, 1986.

Xu, X., Cheng, W., Dudek, D., Hatanaka, M., Cutkosky, M.R., and Full, R. J., “Material Modeling for ShapeDeposition Manufacturing of Biomimetic Components,"ASME Proceedings of DETC/DFM 2000, Baltimore,Maryland, September 10-14, 2000.

Yan, J., Wood, R. J., Avadhanula, S., Sitti, M. and Fearing,R. S., “Towards Flapping Wing Control of aMicromechanical Flying Insect”, IEEE ICRA, SeoulKorea, 2000.

Appendix: Index to Multimedia ExtensionsThe multi-media extensions to this article can be found online by following the hyperlinks from www.ijrr.org.

Table 1: Multimedia Extensions

Extension Media Type

Description

1 video Video showing the first prototype of the "Sprawl" family of hexapedal robots (July 1999).

2 video Video showing the second prototype of the "Sprawl" family of hexapedal robots (built October 1999).

3 video Video showing "Sprawlita," the third prototype of the "Sprawl" family of hexapedal robots (built January 2000). Ground speed on flat terrain exceeds 80cm/s or approximately 5 body-lengths per second.

14

4 video Video showing the basic design of "Sprawlita." Hip servos and wiring and leg pistons are embedded in the structure of the robot. Viscoelastic flexures integrated into the leg struc-tures provide a passive degree-of-freedom at the hip. Pneumatic pis-tons provide the leg's thrusting action, which is controlled open-loop via a fixed activation pattern.

5 video Video showing a sample cycle of Shape Deposition Manufacturing (SDM). In the example, a pneumatic piston, valves, pressure sensor and amplifier circuit and internal passage-ways are embedded in the structure of a prototype linkage. For more information on SDM, please go to http://cdr.stanford.edu/biomimetics.

6 video Video showing a sample sequence for creating a multi-material spatial four-bar linkage. Hard and soft mate-rial is alternately deposited and machined to create a linkage with integrated flexures.

7 video Video showing "Sprawlita" running despite large disturbances. This dis-trubance rejection is accomplished without sensory feedback through the robot's passive properties and open-loop control.

8 video Video showing a sample high-speed movie of "Sprawlita" running (shown at 1/10 normal speed).

9 video Video showing "Sprawlita" overcom-ing hip-height obstacles.

10 video Video showing "Sprawlita" running outdoors, using only a small air hose tether.

11 video Video showing a prototype mecha-nism for extending the stroke length of the robot's hind legs. Assembling this mechanism using conventional off-the-shelf components results in a linkage with numerous small parts that work themselves loose over time. An alternative mechanism that uses the ability of SDM to created parts of rigid material integrated with flexures of visco-elastic material is more compact and robust.

Table 1: Multimedia Extensions

Extension Media Type

Description